I'm not sure I've seen this puzzle before, and I really like it:
We have n keys and n boxes. Each key fits only one box. We shuffle the keys and put one in each box. Then we randomly break open 1≤k≤n boxes. What is the probability that we can unlock all the other boxes?
In reply to @christianp
I'm trying to see if I can turn this into an intuition-challenging result, like the birthday paradox.
"100 boxes, I open 99 of them, prob you can open the last one?" (really high, not surprising)
"100 boxes, I open 1, prob you can open all the rest?" (higher than you'd think?)
In reply to @christianp
The birthday paradox works as a demo because you can engineer an astonishingly high probability from what looks like a small part of the probability space.
Maybe this is the one probability puzzle that *does* match our intuitions.